Many problems are reduced to computation of homotopy groups π*( Hom ((X,x0),(Y,y0))) In the “stable range” i.e. when Y is an Ω-spectrum, the generalized Serre spectral sequence is an important tool. Here we exhibit such a spectral sequence in the “unstable range”. Exemples of computation are given, for sets of L-equivalences, for Haefliger Γ-structure and for homotopy.